Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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TL;DR: A generalized mathematical theory of holor algebra is used to manipulate coefficient arrays needed to generate computational equations which involve elements from throughout the two-dimensional array rather than operating on individual rows and columns.
Abstract: A mathematical development is presented for a direct computation of a two-dimensional fast Fourier transform (FFT). A generalized mathematical theory of holor algebra is used to manipulate coefficient arrays needed to generate computational equations. The result is a set of equations which involve elements from throughout the two-dimensional array rather than operating on individual rows and columns. Preliminary digital computer calculations verify the accuracy of the technique and demonstrate a modest saving of computation time as well.
74 citations
TL;DR: It is shown that a DCT coding scheme reproduces faithfully the seismic waveform at approximately one-third of the original rate, revealing that sinusoidal transforms are well-suited for robust, low-rate seismic signal representation.
Abstract: The authors consider the development and evaluation of transform coding algorithms for the storage of seismic signals. Transform coding algorithms are developed using the discrete Fourier transform (DFT), the discrete cosine transform (DCT), the Walsh-Hadamard transform (WHT), and the Karhunen-Loeve transform (KLT). These are evaluated and compared to a linear predictive coding algorithm for data rates ranging from 150 to 550 bit/s. The results reveal that sinusoidal transforms are well-suited for robust, low-rate seismic signal representation. In particular, it is shown that a DCT coding scheme reproduces faithfully the seismic waveform at approximately one-third of the original rate. >
74 citations
TL;DR: Simulation results indicate that the proposed method outperforms the existing methods in the spectrum accuracy, the range of estimable vibration amplitude/frequency, and the computation complexity.
Abstract: The intricate vibration of a working vehicle provides an important signature to the vehicle type. Small vibrations introduce phase modulation in radar echoes, which is referred to as micro-Doppler (m-D) phenomenon and can be modeled as sinusoidal frequency-modulated (SFM) signal. Such phase modulation induced by vibrations consists of multiple frequency components; moreover, the modulation is usually rather weak. Present parametric estimators are difficult to estimate so many parameters of every frequency component, while nonparametric approaches suffer from low precision. This paper considers the analysis of SFM signal with weak and multiple frequency components modulation on phase term. We first define the SFM signal space to bridge a gap between the SFM signal analysis and classical signal processing methods. Based on the defined signal space, a novel m-D analysis method, i.e., the sinusoidal frequency modulation Fourier transform (SFMFT), is presented. With the operations acting directly on the phase term of SFM signal, SFMFT gives the frequency spectrum of vibration traces. Unlike the existing methods, which apply a sliding short-time window to perform an instantaneous approximation, the proposed method makes use of the global data, which can provide a longer integral period gain, and consequently improves the estimation performance significantly. Simulation results indicate that the proposed method outperforms the existing methods in the spectrum accuracy, the range of estimable vibration amplitude/frequency, and the computation complexity.
74 citations
TL;DR: In this article, a steplike waveform is converted into a duration-limited one which preserves the spectrum of the original waveform and is suitable for discrete Fourier transform (DFT) computations.
Abstract: A steplike waveform which has attained its final value is converted into a duration-limited one which preserves the spectrum of the original waveform and is suitable for discrete Fourier transform (DFT) computations. The method, which is based upon the response of a time-invariant linear system excited by a rectangular pulse of suitable duration, is first applied to continuous waveforms and then to discrete (sampled) waveforms. The difference (errors) between the spectra of a continuous waveform and a discrete representation of it are reviewed.
74 citations
TL;DR: Based on the relation between the ambiguity function represented in a quasipolar coordinate system and the fractional power spectra, the fractionsal Fourier transform (FT) moments are introduced and their applications for signal analysis are discussed.
Abstract: Based on the relation between the ambiguity function represented in a quasipolar coordinate system and the fractional power spectra, the fractional Fourier transform (FT) moments are introduced. Important equalities for the global second order fractional FT moments are derived, and their applications for signal analysis are discussed. The connection between the local moments and the angle derivative of the fractional power spectra is established. This permits us to solve the phase retrieval problem if only two close fractional power spectra are known.
74 citations